Elliptic Curve Cryptography (ECC) was proposed by N. Koblitz and V. Miller independently. ECC has obtained a lot of applications because of smaller key-length and increased theoretical robustness. In ECC, scalar multiplication (or point multiplication) is the operation of calculating an integer multiple of an element in additive group of elliptic curve. In other words, it is a computation of kP for any integer k and a point P on the elliptic curve. To compute EC scalar multiplications, one can easily adapt historical exponentiation methods to scalar multiplication, replacing multiplication by addition and squaring by doubling.
In ECC, elliptic curves over finite fields are used to implement ECDSA and ECE algorithms. There is no known subexponential method and system to solve the elliptic curve discrete algorithm so that the elliptic curves are secure and safe. It is known that an important core operation in the elliptic curves is scalar multiplication. For the last couple of years, many methods have been proposed to reduce the computational complexity of EC scalar multiplications.